The leftist media does play a part in reducing the effectiveness of battle strategies, but they don't take all the blame for demoralizing the troops. Many right wingers are staunchly pro-war but have never even served, so they have no idea the work it takes for soldiers in the field. So on one side you have people saying no war at all costs, and on the other side you have people saying that such and such country deserves to be bombed for its most recent political statement.
The main reason why they are losing morale is because they are fighting an uphill battle that is unwinnable. They are being given a long term strategy that has few assertainable results, and an exit strategy that doesn't include the word "victory". Both the Bush and Obama administrations have the same strategy: toss money and lives at the problem and hope for improvement.
The areas of Afghanistan that are relatively more stable are just temporary quiet zones. Once forces from the Western world pull out, the dissidents will be full on again. The soldiers fighting for freedom in Afghanistan procure one area, only to see car bombs go off and more civilians killed.
The U.S. just wants another satelite power that it can rely on in a pinch, which means defending the current puppet democracy in Afghanistan. Now forces are pushing into Pakistan, and the neo-cons have their eyes on Iran, expecting soldiers to do more grunt work on their selfish behalf; all the while, the staunch left is accusing soldiers and government of being murderers.
Of course they are demoralized.